How do you evaluate $sin ({cos}^{- 1} (\frac{\sqrt{2}}{2}))$ $sin (cos^-1 (sqrt 2/2))$ ?

Question

How do you evaluate $sin ({cos}^{- 1} (\frac{\sqrt{2}}{2}))$ $sin (cos^-1 (sqrt 2/2))$ ?

1 Answer

Impact of this question

16881 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-26T06:20:17

$\frac{\sqrt{2}}{2}$ $sqrt2/2$

Explanation:

$cos (x) = \frac{\sqrt{2}}{2}$ $cos(x)=sqrt2/2$ at $\frac{π}{4}$ $pi/4$ radians therefore $cos (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ $cos(pi/4)=sqrt2/2$

${cos}^{- 1} (cos (\frac{π}{4})) = {cos}^{- 1} (\frac{\sqrt{2}}{2}) \to \frac{π}{4} = {cos}^{- 1} (\frac{\sqrt{2}}{2})$ $cos^-1(cos(pi/4))=cos^-1(sqrt2/2) rarr pi/4=cos^-1(sqrt2/2)$

Sub this into original equation

$sin ({cos}^{- 1} (\frac{\sqrt{2}}{2})) \to sin (\frac{π}{4})$ $sin(cos^-1(sqrt2/2)) rarr sin(pi/4)$

$sin (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ $sin(pi/4)=sqrt2/2$

Science

Math

Humanities

... and beyond

How do you evaluate $sin ({cos}^{- 1} (\frac{\sqrt{2}}{2}))$ $sin (cos^-1 (sqrt 2/2))$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you evaluate sin(cos−1(√22))sin (cos^-1 (sqrt 2/2))?

1 Answer

Explanation:

Related questions

Impact of this question

How do you evaluate $sin ({cos}^{- 1} (\frac{\sqrt{2}}{2}))$ $sin (cos^-1 (sqrt 2/2))$ ?